InterviewSolution
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InterviewSolution
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Die A has 4 red and 2 white faces, whereas die Bhas 2 red and 4 white faces. A coins is flippedonce. If it shows a head, the game continues by throwing die A: if it showstail, then die B is to be used. If the probability that die A is used is32/33 when it is given that red turns up every time in first `n`throws,then find the value of `ndot` |
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Answer» Let R be the event that a red face appears in each of the first n throws. `E_(1):` Die A is used when head has already fallen `E_(2):` Die B is used when tail has already fallen `thereforeP((R)/(E_(1)))=((2)/(3))^(n)and P((R)/(E_(2)))=((1)/(3))^(n)` As per the given condition, `(P(E_(1))P(R//E_(1)))/(P(E_(1))P(R//E_(1))+P(E_(2))P(R//E_(2)))=32/33` `or (1/2((2)/(3))^(n))/(1/2((2)/(3))^(v)+1/2((1)/(3))^(n))=32/33` or `(2^(n))/(2^(n)+1)=32/33` or n = 5 |
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